A genetic algorithm for the steel continuous casting with inter-sequence dependent setups and dedicated machines

The steel continuous casting planning and scheduling problem namely SCC is a particular hybrid (flexible) flowshop that includes stages: (i) the converters (CV), (ii) the refining stands (RS) and (iii) the continuous casting (CC) stages. In this paper we study the SCC with inter-sequence dependent setups and dedicated machines at the last stage. The batch sequences are assumed to be pre-determined for one of the CC devices with a non preemptive scheduling process. The aim is to schedule the batches for each CC machine including the times setup between two successive sequences. We model the problem as a MILP where the objective is to minimize the makespan Cmax that we formulate as the largest completion time taking account of the setup times for each CC. Then, we propose an adapted genetic algorithm that we call Regeneration GA (RGA) to solve the problem. We use a randomly generated instances of several sizes to test the model and for which we do not know an optimal solution. The method is able to solve the problems in an acceptable time for medium and large instances while a commercial solver was able to solve only small size instances.